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Math Problems
Grade 8
Evaluate variable expressions for sequences
Barbara Katzman bought an income property for
$
27
,
000
\$ 27,000
$27
,
000
three years ago. She has held the property for the three years without renting it. If she rents the property out now, what should be the size of the monthly rent payment due in advance if money is worth
7
%
7 \%
7%
compounded annually?
\newline
The size of the monthly rent payment due should be
$
\$
$
□
\square
□
\newline
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
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\newline
Find
(
f
∘
g
)
(
1
)
(f \circ g)(1)
(
f
∘
g
)
(
1
)
for the following functions. Round your answer to two decimal places, if necessary.
\newline
f
(
x
)
=
1
+
x
and
g
(
x
)
=
x
2
+
24
f(x)=1+\sqrt{x} \text { and } g(x)=\sqrt{x^{2}+24}
f
(
x
)
=
1
+
x
and
g
(
x
)
=
x
2
+
24
\newline
Answer
\newline
How to enter your answer (opens in new window)
\newline
(
f
∘
g
)
(
1
)
=
(f \circ g)(1)=
(
f
∘
g
)
(
1
)
=
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Find the
6
6
6
th term of the arithmetic sequence
x
+
5
,
4
x
+
7
,
7
x
+
9
,
…
x+5,4 x+7,7 x+9, \ldots
x
+
5
,
4
x
+
7
,
7
x
+
9
,
…
\newline
Answer:
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Find the slope and
y
y
y
-intercept of the line through the points:
\newline
(
2
,
−
8
)
(2,-8)
(
2
,
−
8
)
and
(
1
,
−
2
)
(1,-2)
(
1
,
−
2
)
\newline
slope
=
=
=
\newline
y
y
y
-intercept
=
=
=
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Find the
51
51
51
st term of the arithmetic sequence
21
,
6
,
−
9
,
…
21,6,-9, \ldots
21
,
6
,
−
9
,
…
\newline
Answer:
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Find the
63
63
63
rd term of the arithmetic sequence
−
17
,
−
11
,
−
5
,
…
-17,-11,-5, \ldots
−
17
,
−
11
,
−
5
,
…
\newline
Answer:
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Triangle FGH is dilated by a scale factor of
6
6
6
to form triangle
F
′
G
′
H
′
\mathrm{F}^{\prime} \mathrm{G}^{\prime} \mathrm{H}^{\prime}
F
′
G
′
H
′
. Side
F
G
\mathrm{FG}
FG
measures
15
15
15
. What is the measure of side
F
′
G
′
\mathrm{F}^{\prime} \mathrm{G}^{\prime}
F
′
G
′
?
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
x
2
cos
(
3
x
)
f^{\prime}(x)=x^{2} \cos (3 x)
f
′
(
x
)
=
x
2
cos
(
3
x
)
. If
f
(
−
2
)
=
−
2
f(-2)=-2
f
(
−
2
)
=
−
2
, then use a calculator to find the value of
f
(
3
)
f(3)
f
(
3
)
to the nearest thousandth.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
x
2
−
4
x
+
2
cos
(
2
x
−
4
)
f^{\prime}(x)=x^{2}-4 x+2 \cos (2 x-4)
f
′
(
x
)
=
x
2
−
4
x
+
2
cos
(
2
x
−
4
)
. If
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
, then use a calculator to find the value of
f
(
6
)
f(6)
f
(
6
)
to the nearest thousandth.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
(
x
2
+
3
)
sin
(
2
x
)
f^{\prime}(x)=\left(x^{2}+3\right) \sin (2 x)
f
′
(
x
)
=
(
x
2
+
3
)
sin
(
2
x
)
. If
f
(
4
)
=
7
f(4)=7
f
(
4
)
=
7
, then use a calculator to find the value of
f
(
−
1
)
f(-1)
f
(
−
1
)
to the nearest thousandth.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
(
x
3
−
1
)
sin
(
x
)
f^{\prime}(x)=\left(x^{3}-1\right) \sin (x)
f
′
(
x
)
=
(
x
3
−
1
)
sin
(
x
)
. If
f
(
4
)
=
3
f(4)=3
f
(
4
)
=
3
, then use a calculator to find the value of
f
(
−
1
)
f(-1)
f
(
−
1
)
to the nearest thousandth.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
x
2
cos
(
3
x
)
f^{\prime}(x)=x^{2} \cos (3 x)
f
′
(
x
)
=
x
2
cos
(
3
x
)
. If
f
(
6
)
=
−
6
f(6)=-6
f
(
6
)
=
−
6
, then use a calculator to find the value of
f
(
2
)
f(2)
f
(
2
)
to the nearest thousandth.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
x
2
cos
(
2
x
+
3
)
f^{\prime}(x)=x^{2} \cos (2 x+3)
f
′
(
x
)
=
x
2
cos
(
2
x
+
3
)
. If
f
(
0
)
=
4
f(0)=4
f
(
0
)
=
4
, then use a calculator to find the value of
f
(
6
)
f(6)
f
(
6
)
to the nearest thousandth.
\newline
Answer:
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